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A stock market comprises 4600 shares of stock A and 1600 shares of stock B. Assume the share prices for stocks A and B are $15 and $30, respectively

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Edufirst

Answer:

  • $8,850

Explanation:

The complete question is:

  • A stock market comprises 4600 shares of stock A and 1600 shares of stock B. Assume the share prices for stocks A and B are $15 and $30, respectively. If you have $15,000 to invest and you want to hold the market portfolio, how much of your money will you invest in Stock A?

Solution

Holding the market portfolio means having the same ratio of shares of stock A and stock B as the market composition.

The market compostion is:

  • 4600 shares stock A / 1600 shares stock B

Naming A the number of shares of stock A and B the number of shares of stock B that you purchase, then your investment will be:

  • $15,000 = $15A + $30B

And the ratio A to B is:

  • A/B=4600/1600 = 23/8

Solve for B and susbtitute in the equation for the investment:

  • B = (8/23)A

  • 15,000 = 15A + 30(8/23)A

To solve multiply the equation by 23 to eliminate the fraction:

  • 345,000 = 345A + 240A
  • 585A = 345,000
  • A = 345,000 / 585 = 589.7

Rounding to the nearest integer that is 590 shares of stock A.

And the amount of money invested in 590 shares of A is the price of the share multiplied by the number of shares:

  • 590 shares × $15 / share = $8,850 ← answer

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